Two wires are fixed on a sonometer wire. Their tensions are in the ratio 8:1, the lengths in the ratio 36:35, the diameters in the ratio 4:1 and the densities in the ratio 1:2. Find the frequency of the beats (in Hz) produced if the note of the higher pitch has frequency of 360 Hz.

For the two wires, we haven1=12l1T1πr12ρ1 and n2=12l2T2πr22ρ2⇒n1n2=l2l1T1T2r2r12ρ2ρ1   …………….(i)According to the given probleml1l2=3635;T1T2=81;r1r2=41 and ρ1ρ2=12Substituting these values in Eq. (1) or  n1n2=353681116⋅21=3536   …………(ii)lt is clear from Eq. (ii) that, has higher pitch so, n2 = 360Now n1360=3536 or n1=350HzThus beat frequency is given asΔn=360−350=10Hz